Condorcet intended to build a mathematical theory of voting from his axiom, just as Euclid had built an entire theory of geometry on his five axioms about the behavior of points, lines, and circles: There is a line joining any two points. Any line segment can be extended to a line segment of any desired length. For every line segment L, there is a circle that has L as a radius. All right angles are congruent to each other. If P is a point and L is a line not passing through P, there is exactly one line through P parallel to L.
